Question: Multiply the following complex numbers, marked as blue dots on the graph: $(6 e^{5\pi i / 6}) \cdot ( e^{\pi i})$ (Your current answer will be plotted in orange.)
Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $6 e^{5\pi i / 6}$ ) has angle $\frac{5}{6}\pi$ and radius $6$ The second number ( $ e^{\pi i}$ ) has angle $\pi$ and radius $1$ The radius of the result will be $6 \cdot 1$ , which is $6$ The angle of the result is $\frac{5}{6}\pi + \pi = \frac{11}{6}\pi$ The radius of the result is $6$ and the angle of the result is $\frac{11}{6}\pi$.